Understanding the Hemisphere
When a sphere is divided along its great circle equator, two congruent solid hemispheres are created. Hemispheres are foundational in architectural dome design, astronomy, and acoustic engineering.
Volume Formula
Because it is exactly half of a full sphere, its volume is calculated as:
V = 2/3 × π × r³
Curved vs Total Surface Area
A solid hemisphere possesses two distinct surfaces: the curved dome and the flat circular base.
- Curved Surface Area: A_curved = 2πr²
- Base Circular Area: A_base = πr²
- Total Surface Area (Solid): A_total = 2πr² + πr² = 3πr²